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{{Infobox ET}} | {{Infobox ET}} | ||
'''56EDF''' is the [[EDF|equal division of the just perfect fifth]] into 56 parts of 12.5349 [[cent|cents]] each, corresponding to 95.7326 [[edo]] | '''56EDF''' is the [[EDF|equal division of the just perfect fifth]] into 56 parts of 12.5349 [[cent|cents]] each, corresponding to 95.7326 [[edo]]. | ||
It is related to the [[regular temperament]] which tempers out [[2401/2400]] and |91 -80 13 2> in the [[7-limit]], which is supported by {{EDOs|383, 670, 1053, 1436, and 1723}} EDOs. | |||
==Related regular temperaments== | |||
===7-limit 383&670=== | |||
Commas: 2401/2400, |91 -80 13 2> | |||
POTE generator: ~|-33 32 -4 -3> = 12.5357 | |||
Mapping: [<1 1 -1 1|, <0 56 318 173|] | |||
EDOs: {{EDOs|383, 670, 1053, 1436, 1723}} | |||
===11-limit 383&670=== | |||
Commas: 2401/2400, 14348907/14348180, 26214400/26198073 | |||
POTE generator: ~13504609503/13421772800 = 12.5359 | |||
Mapping: [<1 1 -1 1 3|, <0 56 318 173 44|] | |||
EDOs: {{EDOs|383, 670, 1053, 1436, 1723}} | |||
== Intervals== | |||
{| class="wikitable" | {| class="wikitable" | ||
! | ! colspan="2" |56ed3/2 | ||
|- | |- | ||
|1 | |1 | ||
| Line 345: | Line 364: | ||
|} | |} | ||
{{todo|inline=1|complete table|text=Add a third column that comments on the intervals, either what [[JI]] they approximate, what they are named, or how they can be used musically.}} | |||
= | |||
Latest revision as of 19:23, 1 August 2025
| ← 55edf | 56edf | 57edf → |
56EDF is the equal division of the just perfect fifth into 56 parts of 12.5349 cents each, corresponding to 95.7326 edo.
It is related to the regular temperament which tempers out 2401/2400 and |91 -80 13 2> in the 7-limit, which is supported by 383, 670, 1053, 1436, and 1723 EDOs.
Related regular temperaments
7-limit 383&670
Commas: 2401/2400, |91 -80 13 2>
POTE generator: ~|-33 32 -4 -3> = 12.5357
Mapping: [<1 1 -1 1|, <0 56 318 173|]
EDOs: 383, 670, 1053, 1436, 1723
11-limit 383&670
Commas: 2401/2400, 14348907/14348180, 26214400/26198073
POTE generator: ~13504609503/13421772800 = 12.5359
Mapping: [<1 1 -1 1 3|, <0 56 318 173 44|]
EDOs: 383, 670, 1053, 1436, 1723
Intervals
| 56ed3/2 | |
|---|---|
| 1 | 12.5349 |
| 2 | 25.0698 |
| 3 | 37.6047 |
| 4 | 50.1396 |
| 5 | 62.67455 |
| 6 | 75.2095 |
| 7 | 87.7444 |
| 8 | 100.2793 |
| 9 | 112.8142 |
| 10 | 125.3491 |
| 11 | 137.884 |
| 12 | 150.4189 |
| 13 | 162.9538 |
| 14 | 175.48875 |
| 15 | 188.2366 |
| 16 | 200.5586 |
| 17 | 213.0935 |
| 18 | 225.6284 |
| 19 | 238.1633 |
| 20 | 250.6982 |
| 21 | 263.2331 |
| 22 | 275.768 |
| 23 | 288.30295 |
| 24 | 300.8379 |
| 25 | 313.3728 |
| 26 | 325.9077 |
| 27 | 338.4426 |
| 28 | 350.9775 |
| 29 | 363.5214 |
| 30 | 376.0473 |
| 31 | 388.5822 |
| 32 | 401.1171 |
| 33 | 413.65205 |
| 34 | 426.187 |
| 35 | 438.7219 |
| 36 | 451.2568 |
| 37 | 463.7917 |
| 38 | 476.3266 |
| 39 | 488.8615 |
| 40 | 501.3964 |
| 41 | 513.9313 |
| 42 | 526.46625 |
| 43 | 539.0012 |
| 44 | 551.536 |
| 45 | 564.071 |
| 46 | 576.6059 |
| 47 | 589.1408 |
| 48 | 601.6757 |
| 49 | 614.2106 |
| 50 | 626.7455 |
| 51 | 639.28045 |
| 52 | 651.8154 |
| 53 | 664.3503 |
| 54 | 676.8852 |
| 55 | 689.4201 |
| 56 | 701.955 |
| 57 | 714.4899 |
| 58 | 727.0248 |
| 59 | 739.5597 |
| 60 | 752.0946 |
| 61 | 764.62955 |
| 62 | 777.1645 |
| 63 | 789.6994 |
| 64 | 802.2343 |
| 65 | 814.7692 |
| 66 | 827.3041 |
| 67 | 839.839 |
| 68 | 852.3739 |
| 69 | 864.9088 |
| 70 | 877.44375 |
| 71 | 889.9787 |
| 72 | 902.5136 |
| 73 | 915.0485 |
| 74 | 927.5834 |
| 75 | 940.1183 |
| 76 | 952.6532 |
| 77 | 965.1881 |
| 78 | 977.723 |
| 79 | 990.25795 |
| 80 | 1002.7929 |
| 81 | 1015.3278 |
| 82 | 1027.8627 |
| 83 | 1040.3976 |
| 84 | 1052.9325 |
| 85 | 1065.4674 |
| 86 | 1078.0023 |
| 87 | 1090.5372 |
| 88 | 1103.0721 |
| 89 | 1115.6071 |
| 90 | 1128.142 |
| 91 | 1140.6769 |
| 92 | 1153.2118 |
| 93 | 1165.7467 |
| 94 | 1178.2816 |
| 95 | 1190.8165 |
| 96 | 1203.3514 |
| 97 | 1215.8863 |
| 98 | 1228.42125 |
| 99 | 1240.9561 |
| 100 | 1253.4911 |
| 101 | 1266.026 |
| 102 | 1278.5609 |
| 103 | 1291.0958 |
| 104 | 1303.6307 |
| 105 | 1316.1656 |
| 106 | 1328.7005 |
| 107 | 1341.23545 |
| 108 | 1353.7704 |
| 109 | 1366.3053 |
| 110 | 1378.8418 |
| 111 | 1391.3751 |
| 112 | 1403.91 |
|
Todo: complete table
Add a third column that comments on the intervals, either what JI they approximate, what they are named, or how they can be used musically. |